$title Test for LindoGlobal's CheckRange Option  (LINDORNG,SEQ=505)
$onText

This test model is based on the chance model from GAMSLIB.

Contributer: Michael Bussieck
Date:        11/19/2010
$offText
$eolCom !
sets f  feeds     / barley, oats, sesame, grnd-meal /
     n  nutrients / protein, fats /
     nn(n) subset of n;

parameters  price(f)  feed prices (fgld per ton) / barley    24.55
                                                   oats      26.75
                                                   sesame    39.00
                                                   grnd-meal 40.50 /
            req(n)    requirements (pct) / protein = 21, fats = 5 /

      table char(*,n,f) feed characteristics (pct)

                 barley    oats     sesame    grnd-meal
mean.protein     12.0      11.9      41.8       52.1
mean.fats         2.3       5.6      11.1        1.3
variance.protein   .28       .19     20.5         .62

variables  x(f)   feed mix (pct)
           cost   total cost per ton
positive variable x;

equations   cdef   cost definition
            mc     mix constraint
            cc(n)  nutrient balance;

cdef..  cost =e= sum(f, price(f)*x(f));

mc..    sum(f, x(f)) =e= 1;

cc(nn(n))..   sum(f, char("mean",n,f)*x(f)) - 1.645*sqrt(sum(f, char("variance",n,f)*sqr(x(f)))) =g= req(n);

models chance chance model        / mc, cc, cdef /

option nlp=lindoglobal, optcr=0; nn(n) = yes;
solve chance minimizing cost using nlp;
parameter xsol(f); xsol(f) = x.l(f);

* Now evaluate at optimum point the ranges
chance.optfile=1; cost.lo=0; ! prevent reformulation
$echo checkrange range.gdx > lindoglobal.opt
solve chance minimizing cost using nlp;

set hdr / lo, hi /;
parameter cdef_cost(hdr)
          cdef_x (f,hdr)
          mc_x   (f,hdr)
          cc_x (n,f,hdr);

Parameter pickf(f);
variable z;
equation defz; defz.. z =e= sum(f$pickf(f), x(f));

model m1 / mc,   defz /;
model m2 / cc,   defz /;
model m3 / cdef, defz /;

* mc
alias (f,ff), (np,n); x.fx(f) = xsol(f);
loop(ff,
  pickf(ff) = 1; x.lo(ff) = 0; x.up(ff)=inf;
  solve m1 min z using nlp; mc_x(ff,'lo') = z.l; if (mc_x(ff,'lo')<-1e12, mc_x(ff,'lo')=-inf);
  solve m1 max z using nlp; mc_x(ff,'hi') = z.l; if (mc_x(ff,'hi')> 1e12, mc_x(ff,'hi')= inf);
  pickf(ff) = 0; x.fx(ff) = xsol(ff));

* cc
nn(n) = no;
loop((np,ff),
  nn(np) = yes; pickf(ff) = 1; x.lo(ff) = 0; x.up(ff)=inf;
  solve m2 min z using nlp; cc_x(np,ff,'lo') = z.l; if (m2.modelstat=18 or cc_x(np,ff,'lo')<-1e12, cc_x(np,ff,'lo')=-inf);
  solve m2 max z using nlp; cc_x(np,ff,'hi') = z.l; if (m2.modelstat=18 or cc_x(np,ff,'hi')> 1e12, cc_x(np,ff,'hi')= inf);
  nn(np) = no;  pickf(ff) = 0; x.fx(ff) = xsol(ff));

* cdef
cost.fx = cost.l;
loop(ff,
  pickf(ff) = 1; x.lo(ff) = 0; x.up(ff)=inf;
  solve m3 min z using nlp; cdef_x (ff,'lo') = z.l; if (cdef_x (ff,'lo')<-1e12, cdef_x (ff,'lo')=-inf);
  solve m3 max z using nlp; cdef_x (ff,'hi') = z.l; if (cdef_x (ff,'hi')> 1e12, cdef_x (ff,'hi')= inf);
  pickf(ff) = 0; x.fx(ff) = xsol(ff));
cost.lo=0; cost.up=inf;
solve m3 min cost using nlp; cdef_cost('lo') = cost.l; if (cdef_cost('lo')<-1e12, cdef_cost('lo')=-inf);
solve m3 max cost using nlp; cdef_cost('hi') = cost.l; if (cdef_cost('hi')> 1e12, cdef_cost('hi')= inf);

execute_unload 'rangeWant.gdx' cdef_cost, cdef_x, mc_x, cc_x;
execute 'gdxdiff range.gdx rangeWant.gdx Eps=1e-4 > %system.nullfile%';
abort$errorlevel 'range.gdx and rangeWant.gdx differ';